摘要在中学期间，困扰学生最多的问题一定是最值问题。类比自己中学时期的学习经验和调查 结果我发现，大多数的中学生对于这块知识的学习兴趣不高。而学生对于这块知识缺乏兴趣 的主要原因是因为这部分的知识太零散，并且与其他的数学知识点以及生活中的情境结合密 切，较难找到一个统一的方法去解决这类问题，而它的练习题难度较大，往往自己在解题的 时候花费的时间很大，正确率不高。88103

另一方面，随着社会的发展，科技的进步，最值的求解会更加方便、更快速、更清晰地帮 助我们解决问题。渐渐地形成了数学一个重要的分支——运筹学与最优化。所以中学打下一 个坚实的基础是很有必要的。纵观目前关于这方面的文章，很大的部分都是作为期刊出现只 是总结了其中的一小块知识及其计算方法，缺少一个很系统的总结和探究。本文试着从知识 板块作为区分，概括总结各个中学知识点中最值问题的常见形式以及解决方法。并且将最值 问题的知识进行拓展，让其与运筹学中的部分内容建立联系。希望本文对于中学最值问题知 识的教学以及梳理起到积极的作用。

毕业论文关键词：最值问题； 中学数学； 典型案例； 拓展研究

Abstract In secondary school, extreme-value problems are the most puzzled problems for students。 Analogizing the writer’s own experience in secondary school with some researches, the writer found that most students in secondary school are not so interested in extreme-value problems。 The reason that leads to such circumstance is that the knowledge points related with extreme-value problems are unsystematic and entwined with other knowledge points in mathematics as well as some situations in real life。 Therefore, it is hard to solve all this kind of problems in a unified way。

Because of the high degree of extreme-value problems, solving this kind of problems usually takes a lot of time, and the correct rate is not high。

Meanwhile, with the development of society and the progress of science and technology, the way to solve extreme-value problems becomes faster and more convenient, and gradually there forms an important branch of mathematics, which is called operational research and optimization。 Therefore, it is necessary to lay a solid foundation in secondary school。 Referring to the current articles on this aspect in some journals, most of them are only a summary of knowledge related with

extreme-value problems and its calculation method, which lacks of a very systematic summary and exploration。 In this paper, the knowledge related with extreme-value problems would be classified into different sections, and the common forms and solutions of the extreme-value problems would be summarized。 Further more, the knowledge related with extreme-value problems would be expanded and the connections with some parts of the operational research would be established。 It is hoped that this paper will positively influence the teaching processes in secondary school on extreme-value problems。

Key words: Extreme-value problems; secondary school; typical cases; further study

目 录源-于,优W尔Y论L文.网wwW.youeRw.com 原文+QQ75201,8766

摘要 1

目录 2

1。绪论 3

1。1 问题的提出 3

1。2 目前研究现状 3

1。3 研究背景 3

1。4 研究意义 3

2。  中学数学中主要的最值问题及解法 3